Acceptable-and-attractive Approximate Solution of a Continuous Non-Cooperative Game on a Product of Sinusoidal Strategy Functional Spaces

IF 1.8 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Foundations of Computing and Decision Sciences Pub Date : 2021-06-01 DOI:10.2478/fcds-2021-0012
V. Romanuke
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引用次数: 1

Abstract

Abstract A problem of solving a continuous noncooperative game is considered, where the player’s pure strategies are sinusoidal functions of time. In order to reduce issues of practical computability, certainty, and realizability, a method of solving the game approximately is presented. The method is based on mapping the product of the functional spaces into a hyperparallelepiped of the players’ phase lags. The hyperparallelepiped is then substituted with a hypercubic grid due to a uniform sampling. Thus, the initial game is mapped into a finite one, in which the players’ payoff matrices are hypercubic. The approximation is an iterative procedure. The number of intervals along the player’s phase lag is gradually increased, and the respective finite games are solved until an acceptable solution of the finite game becomes sufficiently close to the same-type solutions at the preceding iterations. The sufficient closeness implies that the player’s strategies at the succeeding iterations should be not farther from each other than at the preceding iterations. In a more feasible form, it implies that the respective distance polylines are required to be decreasing on average once they are smoothed with respective polynomials of degree 2, where the parabolas must be having positive coefficients at the squared variable.
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正弦策略函数空间乘积上连续非合作对策的可接受且有吸引力的近似解
摘要考虑了一个求解连续非合作对策的问题,其中玩家的纯策略是时间的正弦函数。为了减少实际可计算性、确定性和可实现性的问题,提出了一种近似求解博弈的方法。该方法基于将函数空间的乘积映射到玩家相位滞后的超平行投影中。然后,由于均匀采样,用超立方体网格代替超平行网格。因此,初始博弈被映射到一个有限的博弈中,其中玩家的支付矩阵是超三次的。近似是一个迭代过程。沿着游戏者的相位滞后的间隔的数量逐渐增加,并且求解相应的有限对策,直到有限对策的可接受解变得足够接近于先前迭代中的相同类型的解。足够接近意味着玩家在后续迭代中的策略彼此之间的距离不应比之前的迭代更远。在一种更可行的形式中,这意味着一旦用相应的2次多项式对相应的距离多段线进行平滑,就要求它们平均递减,其中抛物线在平方变量处必须具有正系数。
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来源期刊
Foundations of Computing and Decision Sciences
Foundations of Computing and Decision Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-
CiteScore
2.20
自引率
9.10%
发文量
16
审稿时长
29 weeks
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